After execute create method, use valid variantId to execute request as "https://developers.google.com/android-publisher/api-ref/rest/v3/systemapks.variants/download" suggested, no error pops up and nothing is downloaded.
service = build('androidpublisher', 'v3', http=http_auth, cache_discovery=False)
variant = service.systemapks().variants().download(packageName=package_name, versionCode=version_code, variantId=variant_id).execute()
You should add "&alt=media" to the URL, like this:
https://www.googleapis.com/androidpublisher/v3/applications/<package_name>/systemAPKs/<version_code>/variants/<variant_id>:download?alt=media
Then the request body will contain the binary of the APK.